docstr: Multistep solver DPM-Solver-2 from time `t_prev_list[-1]` to time `t`.
  Args:
      x: A pytorch tensor. The initial value at time `s`.
      model_prev_list: A list of pytorch tensor. The previous computed model values.
      t_prev_list: A list of pytorch tensor. The previous times, each time has the shape (x.shape[0],)
      t: A pytorch tensor. The ending time, with the shape (x.shape[0],).
      solver_type: either 'dpm_solver' or 'taylor'. The type for the high-order solvers.
          The type slightly impacts the performance. We recommend to use 'dpm_solver' type.
  Returns:
      x_t: A pytorch tensor. The approximated solution at time `t`.
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code: def multistep_dpm_solver_second_update(
      self, x, model_prev_list, t_prev_list, t, solver_type="dpm_solver"
  ):
      """
      Multistep solver DPM-Solver-2 from time `t_prev_list[-1]` to time `t`.
      Args:
          x: A pytorch tensor. The initial value at time `s`.
          model_prev_list: A list of pytorch tensor. The previous computed model values.
          t_prev_list: A list of pytorch tensor. The previous times, each time has the shape (x.shape[0],)
          t: A pytorch tensor. The ending time, with the shape (x.shape[0],).
          solver_type: either 'dpm_solver' or 'taylor'. The type for the high-order solvers.
              The type slightly impacts the performance. We recommend to use 'dpm_solver' type.
      Returns:
          x_t: A pytorch tensor. The approximated solution at time `t`.
      """
      if solver_type not in ["dpm_solver", "taylor"]:
          raise ValueError(
              "'solver_type' must be either 'dpm_solver' or 'taylor', got {}".format(
                  solver_type
              )
          )
      ns = self.noise_schedule
      dims = x.dim()
      model_prev_1, model_prev_0 = model_prev_list
      t_prev_1, t_prev_0 = t_prev_list
      lambda_prev_1, lambda_prev_0, lambda_t = (
          ns.marginal_lambda(t_prev_1),
          ns.marginal_lambda(t_prev_0),
          ns.marginal_lambda(t),
      )
      log_alpha_prev_0, log_alpha_t = ns.marginal_log_mean_coeff(
          t_prev_0
      ), ns.marginal_log_mean_coeff(t)
      sigma_prev_0, sigma_t = ns.marginal_std(
          t_prev_0
      ), ns.marginal_std(t)
      alpha_t = torch.exp(log_alpha_t)
  
      h_0 = lambda_prev_0 - lambda_prev_1
      h = lambda_t - lambda_prev_0
      r0 = h_0 / h
      D1_0 = expand_dims(1.0 / r0, dims) * (model_prev_0 - model_prev_1)
      if self.predict_x0:
          if solver_type == "dpm_solver":
              x_t = (
                  expand_dims(sigma_t / sigma_prev_0, dims) * x
                  - expand_dims(alpha_t * (torch.exp(-h) - 1.0), dims)
                  * model_prev_0
                  - 0.5
                  * expand_dims(alpha_t * (torch.exp(-h) - 1.0), dims)
                  * D1_0
              )
          elif solver_type == "taylor":
              x_t = (
                  expand_dims(sigma_t / sigma_prev_0, dims) * x
                  - expand_dims(alpha_t * (torch.exp(-h) - 1.0), dims)
                  * model_prev_0
                  + expand_dims(
                      alpha_t * ((torch.exp(-h) - 1.0) / h + 1.0), dims
                  )
                  * D1_0
              )
      else:
          if solver_type == "dpm_solver":
              x_t = (
                  expand_dims(
                      torch.exp(log_alpha_t - log_alpha_prev_0), dims
                  )
                  * x
                  - expand_dims(sigma_t * (torch.exp(h) - 1.0), dims)
                  * model_prev_0
                  - 0.5
                  * expand_dims(sigma_t * (torch.exp(h) - 1.0), dims)
                  * D1_0
              )
          elif solver_type == "taylor":
              x_t = (
                  expand_dims(
                      torch.exp(log_alpha_t - log_alpha_prev_0), dims
                  )
                  * x
                  - expand_dims(sigma_t * (torch.exp(h) - 1.0), dims)
                  * model_prev_0
                  - expand_dims(
                      sigma_t * ((torch.exp(h) - 1.0) / h - 1.0), dims
                  )
                  * D1_0
              )
      return x_t
  
imports: import math
  import torch
  from tqdm import tqdm
label_desc: Use image node_id 11 for calling the DPM_Solver obj's underlying member method code with example usage: obj.multistep_dpm_solver_second_update(x, model_prev_list, t_prev_list, t, solver_type) and returns: x_t